(1) Field of Invention
The present invention is related to an imaging system and, more specifically, to a system for denoising synthetic aperture radar (SAR) images via sparse and low-rank decomposition (SLR) and using SAR images for imaging a complex scene.
(2) Description of Related Art
Synthetic aperture radar (SAR) images can be useful for a variety of purposes, including object image reconstruction. A problem with existing SAR systems; however, is that they are not capable of handling complex scene SAR imaging. In other words, the conventional methods do not deal well with noise without blurring.
By way of example, one group of researchers proposed the filtered back projection method that typically generates SAR images that are noisy, especially when the scene is complex (see the List of Incorporated Literature References, Literature Reference No. 4). Therefore, to obtain high-resolution images, they require significant amount of phase history data and, as a result, the reconstructed images become blurry. In addition, these methods are not able to handle imperfect data, such as when there is missing data.
Other researchers (see Literature Reference Nos. 5 and 6) proposed sparsity- or regularization-based methods, which are more flexible in terms of imperfect data. By adding certain additional constraints, the inverse problems become well conditioned. The target scene can be reconstructed with high fidelity. These methods are however limited to images that are sparse in some known transform domain. Real scenarios typically contain targets in complex scenes. Therefore, regularization-based methods cannot be applied to many real-world scenarios.
Current methods only attempt to reconstruct single images instead of batch processing. Alternatively, Sparse and low-rank (SLR) imaging was applied to dynamic scenes that consist of moving point targets and stationary point targets (see Literature Reference No. 1). In particular, SLR is applied to the echoes of the point targets after pre-processing to separate moving targets from stationary targets. The pre-processing step consists of pulse and range compression and windowing in order to form the echoes of stationary targets as a low-rank matrix and the echoes of moving targets as a sparse matrix. This method can deal with multiple moving targets with different velocity. However, the preprocessing step in the paper was demonstrated through analysis of synthetic scenario and didn't address the discretization issue. Moreover, the method requires a significant amount of phase history data. Data with 360° azimuth angles were demonstrated for separating the moving targets from the stationary ones. Further, such a method assumes that the background consists of a few stationary point targets and does not work well with noisy scenes.
Other researchers proposed a method for forming SAR images of moving targets without the knowledge of the target motion (see Literature Reference No. 8), The method uses a processing kernel that involves a one-dimensional interpolation of the de-ramped phase history. The estimated motion parameters from the SAR target data are then used to compensate the quadratic and higher order target phase to focus the moving target. However, it is difficult to get a good estimate because of the insufficient contrast of the target and the background.
Another researcher took a sparsity-based approach to address the issues related to the phase of the complex-valued SAR reflectivity (see Literature Reference No. 9). The phase errors in the phase history data can cause the formed imagery defocused. Their method is a joint imaging and phase error correction sparsity-driven framework. This is then extended to handle moving targets in the scene, which also leads to phase errors. However, this framework assumes the scenes have sparse representations and only demonstrates on simple synthetic scenes. The method cannot be generalized for complex scenes.
Thus, a continuing need exists to use SLR to reconstruct SAR images and use SAR imaging to handle complex scenes.